The NRSfM problem is known [1]} to be ill-posed if no assumption is made on \(\mathrm {S}_i\) . Bregler et al. [2]} make a widely-accepted assumption that \(\mathrm {S}_i\)  of all frames are a linear combination of \(K\)  basis shapes \(\mathrm {B}_{k} \in \mathbb {R}^{3 \times P}\) , which is:
\(\mathrm {S}_{i} = \sum _{k=1}^{K} (c_{i,k}\otimes \mathrm {I}_3)\mathrm {B}_k,\) 
